Audiences were charmed by the antics of its star turn, terrier Uggie, and many have now contacted the charity in search of their own canine leading man.

Almost 630 people looked on the Battersea website for a jack russell when the Baftas took place on 12 February – more than double the number who browsed the website specifically for this breed on the previous Sunday, and more than any other night of the year so far.

In the week following the Baftas, jack russells were the second most popular breed rehomed by Battersea, beaten only by Staffordshire bull terriers, of which there are many more in the charity's three homes. Before the Baftas, jack russells were the fifth most common breed to find new owners through Battersea in February.

With the Oscars taking place this Sunday, the home is bracing itself for another peak in demand and is hoping its current jack russell residents will find new owners. Last year, jack russells made up 8.4% of the dogs who came into Battersea.

Battersea's rehoming co-ordinator Carly Perry said: "Jack russells are always a popular breed here at Battersea, but this current increase in demand is giving them the opportunity to really enjoy their fame.

"Although we're pleased about this, we want to make sure people who do rehome their own Uggie are aware of the level of commitment required to own a pet, so their new four-legged friend can enjoy being the main attraction in a new home."

She added: "Deciding to take home an animal is a lifelong commitment – which in some cases can span to around 15 years – and your pet will require daily care and attention to be happy and healthy. Potential owners need to understand the breed and ensure they can provide the right environment for these dogs."

The Jack Russell Terrier Club of America warned that many dog owners, even experienced ones, are sometimes overwhelmed by the demands of looking after the dogs, "leading to them being abandoned even before they reach adulthood. Russells are first and foremost hunting dogs. The traits and skills that make them excellent hunting dogs – digging, barking, an aggressive nature and an ability to follow scent – are often interpreted as bad habits that cause people to give them up."

It added: "Today, jack russell terriers are hot! Tomorrow, those of us who are truly devoted to the breed will be paying the price for this surge in popularity with greatly increased use of our rescue system."

Uggie himself nearly ended up in a dog pound after being rejected by his first two owners for being too wild. He was adopted by animal trainer Omar Von Muller who only intended to foster the dog while finding him a new home, but decided to train him instead after finding Uggie to be smart and brave.

At the 2011 Cannes film festival Uggie won the Palm Dog award for his performance in The Artist, but Bafta decided the dog lacked the essential attribute of being a human and was therefore not qualified to compete in its 2012 awards. Nevertheless, an editor at the website Movieline began a campaign called Consider Uggie on Facebook to seek recognition for his performance in the Oscars, saying that while the dog wasn't as good as George Clooney in The Descendants, he outperformed Leonardo DiCaprio in J Edgar.